If you don't want to muck it up you need to disassemble as much as possible. You want the enclosure by itself, sans speaker, foam, ear cup, headband, etc.
If you want to do a pro job you will need to sand the plastic to rough it up, you don't have to sand the current paint off but you need something it can adhere to. Once you get it a little roughed up, clean it with a towel and alcohol or finger nail polish remover (acetone). This removes oils and residue. Blow it clean with a can of air duster and you're ready to paint.
1. Primer. This helps the actual paint adhere better and makes the paint job more durable and the tone more even. You will want to use spray paint. I used auto paint when I did my PC case but you can use just about anything but latex house paint. Acryllics are really good and durable, quick drying.
2. Hang the enclosures on little bits of wire or string so you don't have to touch them, wire is better because it's stiff and you can control spin. Use light and even coats of primer. Let it dry a minimum of 20 minutes in between coats, you don't want to see any drops running, use light coats, and use many. Don't rush it or it won't dry fast enough and you will get runs. Do 2 or 3 coats this way. If it's humid and cold where you're at let it dry longer, 30-45 min between coats.
3. After the primer is done let it dry over night 24hours min. If you have a blow dryer you can speed that up by blow drying on low heat for 10-15 minutes once it's dry enough to handle. You're trying to get the solvent to evaporate, leaving a solid shell of primer.
4. Now do the same thing again except with paint. If you wish to do multiple tones, or not paint in some areas, use masking tape and a razer blade to create masks. If you want to add pin stripping you can do that by hand later.
When you've done enough thin coats of paint that the color is solid enough for you, let it dry overnight again or blow dry once dry enough to handle.
The last step if you want a really good finish is to apply an acrylic sealant, even polyurethane sealant will work well. Except now you're going to lightly sand in between coats of sealant. You are trying to make the finish as smooth as possible, use very fine grit sand paper and LIGHTLY sand. Use 2 - 3 coats not sanding the last coat and you're done.
Congratulations, you have a professional paint job that will last as long as you have the headphones. The paint won't rub off on you, won't peel, won't flake, won't bubble, it will be as good as the factory finish.